Radio Frequency Identification (RFID) is an automatic identification system that uses wireless communications to identify objects. Nowadays, large amounts of RFID tags are used in supply chains for product identification or sensor networks, especially, where the cost and energy are critical.
Recently the number of applications that use RFID technology have increased, and the reading speed became one of the most critical issues in these applications.
In RFID systems, the tags typically share a common communications channel. Thus, there is a certain probability of tag-collisions, i.e. multiple tags answering simultaneously. This collision probability naturally increases in dense networks with many tags. Since passive tags are the most practical tags in the market, because of their low price and simple design, they cannot sense the channel or communicate with the other tags. As a result, the reader is responsible for coordinating the network and has to avoid tag collisions using specific anti-collision algorithms.
The conventional anti-collision algorithm is the Framed Slotted ALOHA (FSA) algorithm [1], which is only a Medium Access Control (MAC) layer protocol. In such systems, only the answer of a single tag is considered as a successful slot, and if multiple tags respond simultaneously, a collision occurs. Then all the replied tags of this slot are discarded.
The performance of FSA-based protocols is maximized by adapting the frame length L to the number of RFID tags n. The frame length or frame size L specifies the number of slots associated with the amount of time or frame the RFID reader is waiting for responses of the RFID tags after submitting the request signal to the RFID tags.
However, in practical applications, the number of tags n in the interrogation region is unknown.
Furthermore, the number of tags n may even vary, e. g., when the tags are mounted on moving goods.
Therefore, so called Dynamic Framed Slotted ALOHA (DFSA) [2] is commonly used.
DFSA first estimates the number of tags in the interrogation area, and then calculates the optimal frame size L for the next reading cycle. Therefore, the system performance is controlled by how precise and fast the number of tags in the interrogation area is estimated.
Simple estimation methods have been proposed by Vogt [2] and Schoute [3].
The lower bound estimation method proposed by Vogt [2] states that the remaining number of tags is double the number of collided slots in the previous frame.
Schoute [3] proposed a posteriori expected factor of 2.39 to estimate the number of tags in the interrogation area.
However, both methods depend only on a single information which is the number of collided slots. Therefore, they increase the tags estimation error in dense networks [4].
The author of [1] proposed a more complex estimation method minimizing the distance between the observed empty Eobs, successful Sobs, and collided Cobs slots and the expected values E, S, C for a given frame length L.
This is to be done via the following formula:
            ɛ      conv        ⁡          (              L        ,                  S          obs                ,                  C          obs                ,                  E          obs                    )        =            min      n        ⁢          {                                              E            -                          E              obs                                                +                                        S            -                          S              obs                                                +                                        C            -                          C              obs                                                    }      
However, this method involves numerical searching to find the optimum value of n.
Moreover, it is assumed that the responses of the tags are identically distributed in the slots, which is generally not an accurate assumption.
Another approach is given by [5]. It is assumed that tags in the frame are distributed using the binomial model. Once the values of the empty (E), successful (S), and collided slots (C) are obtained for a given number of time slots L, a posteriori distribution is calculated. Afterwards, the number of tags n is searched which maximizes the given a posteriori probability.
An improved version including the mutual dependence of different slot types (empty, successful, and collided) is presented in [6]. However, this method is more complex and needs more iterations to find the optimum value of n. Moreover, it does not improve the performance of the FSA compared to the proposal in [5].
In [4] the same approach as in [5] is used but based on the Poisson model instead of the binomial model. This is done in order to obtain a less complex equation and to decrease the searching complexity. However, it still needs iterations of searching to obtain the optimum value of n.
Proposals including a closed form solution for estimating the number of tags n without need for searching iterations are given by [7, 8]. However, both methods used numerical interpolations to reach to the optimum value of n. Therefore, both result equations cannot be used utilizing further parameters like the collision recovery probability which will be discussed later.
A different aspect worth to be considered is the following.
Modern RFID systems have the capability to convert some collided slots into successful slots. In such systems, the number of collided and successful slots delivered to the MAC layer are not accurate information about the real number of tags at the reading area. Therefore, the collision recovery probability α should be taken into consideration.
In [9], for an estimation approach of [1], the collision recovery probability α was taken into consideration. However, this method leads to a multi-dimensional searching, which is time consuming and has a high complexity. And there still remains the accuracy problem underlying the method according to [1].